Question

Compute the least-squares regression equation for the given data set. Round the slope and y-intercept to at least four decimal places. х 3 7 5 4 y اقتها 1 6 4 5 Send data alle Regression line equation: y

Answer 1

Solution :

X	Y	XY	X2	Y2
6	3	18	36	9
3	1	3	9	1
7	6	42	49	36
5	4	20	25	16
4	5	20	16	25

n	5
sum(XY)	103.00
sum(X)	25.00
sum(Y)	19.00
sum(X^2)	135.00
sum(Y^2)	87.00

Now ,

Slope of the regression line is

b = ΠΣxy - (Σκ) Σy) ΠΣχ2 - (Σx)2

  $\therefore$ b = 0.8000

Now , y intercept of the line is

a = Σy - bΣΧ n

  $\therefore$ a = -0.2000

The equation of the regression line is

$\hat y$ = a + bx

$\hat y$ = ( -0.2000) + 0.8000x